Intersecting functions
The exercise appears under the Algebra II Math Mission and Mathematics III Math Mission. This exercise helps to understand intersection of function via their T-tables and graphs. Types of Problems There are three types of problems in this exercise: # Use the table to determine possible solutions: This problem provides a t-table for two functions and a collection of possible solutions. The student is asked to use the table to select all the options from the collection that could be the solution to the intersection of the functions. # Classify each input in the chart: This problem has graphs of two functions, labeled points, and a chart. The student is asked to determine which values are solutions to the individual equations, and to the intersection of the functions. # Approximate the solutions from the graphs: This problem has a graph of two functions. The student is asked to use the graph to approximate the solutions within 0.2 units. Strategies Knowledge of the different views of a function are encouraged to ensure success on this exercise. # On Use the table to determine the possible solutions the solution will occur in the interval where one function changes from being larger than the other to smaller, or vice versa. # On Classify each input in the chart there generally seems to be one solution to each function's zeros, and two solutions to their intersection. Also, one answer is a "nothing." Real-life Applications # Situations with multiple constraints need to satisfy them simultaneous. Systems are a method of doing so. # Often data collected through experimentation does not have a precise algebraic form. The strategies developed in this exercise can be used to analyze these type of situations. # Money as a function of time. One never has more than one amount of money at any time because they can always add everything to give one total amount. By understanding how their money changes over time, they can plan to spend their money sensibly. Businesses find it very useful to plot the graph of their money over time so that they can see when they are spending too much. # Temperature as a function of various factors. Temperature is a very complicated function because it has so many inputs, including: the time of day, the season, the amount of clouds in the sky, the strength of the wind, and many more. But the important thing is that there is only one temperature output when they measure it in a specific place. # Location as a function of time. One can never be in two places at the same time. If they were to plot the graphs of where two people are as a function of time, the place where the lines cross means that the two people meet each other at that time. This idea is used in logistics, an area of mathematics that tries to plan where people and items are for businesses. Category:Math exercises Category:Algebra II exercises Category:Algebra II: Systems of equations and inequalities Category:Mathematics III exercises